INF3110/4110
                   exercises week 44 (30.10 - 3.11.2006)



Exercise 1 
-----------

Given the following facts in Prolog:
    p(anne, aase, aale, 1960).
    p(arne, aase, aale, 1962).
    p(beate, anne, lars, 1989).
    p(bjorn, lise, arne, 1990).

1. Give rules for the relation gc(X,Y) which expresses that X is a
   grandchild of Y.  


2. What will the result be of executing the queries: 
   gc(beate, aale) 
   and
   gc(beate, X).

3. Give rules for the relation cd(X,Y) which expresses that X and Y
   have common descendants. (i.e. children, grandchildren, great grand
   children etc.)

4. Give rules for the relation oc(X) which expresses that X is an only
   child (enebarn).


Exercise 2
-----------

a) IN211 exam 1992, problem 2e:

1. How would you express the following facts in Prolog: "eva is anne's
boss", "eva is atle's boss" and "lars is eva's boss".
 
2. We introduce the relation sup, such that sup(X,Y) means that X is
superior to Y, i.e. X is the boss of Y or the boss of the boss of
Y. Give prolog rules which defines the sup relation. 

3. A collection of "boss"-facts is said to be OK if no person is
superior to himself and if no person have more than one boss. Show how
you can test that your facts are OK. 
 

b) IN211 exam 1997, problem 3:

We consider some form for data storage divided in two, a local storage
and a remote storage. (As. e.g. with memory and disk in a computer). 

The content of the local store and the remote store is expressed by
the relation ls and rs, respectively. E.g. by the following facts: 

ls(1, ole).
ls(2, dole).
ls(3, ole).

rs(1, ole).
rs(2, dole).
rs(3, doffen).
rs(5, dolly).

The first argument of ls and rs are called indexes, the second
argument is called values.

- Look up
 
Write rules which describe a relation "find" such that find(I,X) is
true if either ls(I,X) or rs(I,X) is true. If there are several
solutions, ls solutions should come before rs solutions. 

- Error

Write rules which describe a relation "error" such that error(I) is
true if there for some index I are different values in rs and ls. 
Index 3 is for example wrong in the facts given above.

- Multiple 

Write rules to describe a relation "multi" such that multi(X) is true
if X occurs more than once in ls, or in rs, or if X occurs in both rs and ls, but
with different indexes. 

How many solutions will multi(X) give (including repeated solutions),
for the facts given above? 

c) INF3110/4110 exam 2003 problem 6.
   (http://www.uio.no/studier/emner/matnat/ifi/INF3110/h06/gamle_eksamen/INF3110-4110-2003-eks-eng.pdf)


Exercise 3
-----------

Write a Prolog rule 
	addAtEnd(List1, Object, List2)
which is true if List2 is List1 extended with Object at the end. 


Exercise 4
----------

Write a Prolog rule to reverse a list.